Non-orthogonal one-step calibration method for robotized transcranial magnetic stimulation

Robotized transcranial magnetic stimulation (TMS) combines the benefits of neuro-navigation with automation and provides a precision brain stimulation method. Since the coil will normally remain unmounted between different clinical uses, hand/eye calibration and coil calibration are required before each experiment. Today, these two steps are still separate: hand/eye calibration is performed using methods proposed by Tsai/Lenz or Floris Ernst, and then the coil calibration is carried out based on the traditional TMS experimental step. The process is complex and time-consuming, and traditional coil calibration using a handheld probe is susceptible to greater calibration error.

A novel one-step calibration method has been developed to confirm hand/eye and coil calibration results by formulating a matrix equation system and estimating its solution. Hand/eye calibration and coil calibration are performed to confirm the pose relationships of the marker/end effector 'X', probe/end effector 'Y', and robot/world 'Z'. First, the coil is fixed on the end effector of the robot. During the one-step calibration process, a marker is mounted on the top of the coil and a calibration probe is fixed at the actual effective position of the coil. Next, the robot end effector is moved to a series of random positions 'A', the tracking data of marker 'B' and probe 'C' is obtained correspondingly. Then, a matrix equation system AX = ZB and AY = ZC can be acquired, and it is computed using a least-squares approach. Finally, the calibration probe is removed after calibration, while the marker remains fixed to the coil during the TMS experiment. The methods were evaluated based on simulation data and on experimental data from an optical tracking device. We compared our methods with two classical methods: the QR24 method proposed by Floris Ernst and the handheld coil calibration method.

The new methods outperform the QR24 method in the aspect of translational accuracy and performs similarly in the aspect of rotational accuracy, the total translational error decreased more than fifty percent. The new approach also outperforms traditional handheld coil calibration of navigated TMS systems, the total translational error decreased three- to fourfold, and the rotational error decreased six- to eightfold. Furthermore, the convergence speed is improved 16- to 27-fold for the new algorithms.

These results suggest that the new method can be used for hand/eye and coil calibration of a robotized TMS system. Two complex steps can be simplified using a least-squares approach.